What is Heterogeneous Fleet Vehicle Routing Problem (HFVRP)? [Types and Examples]

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What is heterogeneous fleet vehicle routing problem

What is Heterogeneous Fleet Vehicle Routing Problem (HFVRP)?

The Heterogeneous Fleet Vehicle Routing Problem (HFVRP) is a logistics-related problem that needs to find the best route to allocate a fleet of vehicles with varying characteristics to provide goods or services to consumers who are spread out across multiple locations.

The varying capacities, sizes, and expenses of the vehicles are taken into consideration as routes are optimized to reduce cost and time. It is a variant of the Vehicle Routing Problem (VRP) that is a well-known problem in the field of operations research. 

HFVRP is important as it helps businesses to streamline their delivery operations, save time and money, reduce fuel consumption, and boost customer satisfaction. 

Types of Constraints in HFVRP

The HFVRP considers several types of constraints to guarantee that the resultant routes are effective and practical. Some of them include:

1. Capacity constraints

One of the most prevalent constraints in the HFVRP is the capacity constraint. There is a maximum capacity for each vehicle in the fleet, which restricts the volume of cargo or services it may transport. Each vehicle should only have the total number of goods or services assigned to it; otherwise, the vehicle won’t be able to complete the route.

2. Time window constraints

The time window constraint in the HFVRP is yet another crucial restriction. There is a defined window of time each customer may receive delivery. The delivery will be considered late if the vehicle does not show up within this window of time. To guarantee that clients receive deliveries at their convenient time, time window restrictions are required.

3. Route length constraints

Another restriction that must be taken into account in the HFVRP is the length of each route. Each vehicle has a set maximum travel distance, and the combined distance covered by all vehicles shouldn’t go over this limit. This restriction is necessary to avoid long-distance travel by automobiles, which can raise fuel prices, maintenance costs, and trip times.

4. Precedence constraints

Some clients could be reliant on other clients or places. Priority restrictions make sure that in these situations, vehicles visit the dependent customers before the dependent sites. For instance, if a customer needs a part that is accessible from another place, the truck must first travel to that site before returning the part and delivering it to the customer.

5. Cost constraints

Finally, cost restrictions are also crucial in the HFVRP. The cost of operating each vehicle in the fleet is different and includes both fixed and variable expenses like gasoline, upkeep, and driver salaries. To make sure the logistics operation is profitable, the overall cost of the route shouldn’t go over a certain budget.

To sum up, HFVRP contains several restrictions to ensure that vehicles travel on effective routes. Additionally, to find routes that minimize overall costs and maximize the effectiveness of the logistics operation, the optimization algorithms that take into account these constraints should be considered.

HFVRP Formulation & Solution Methods 

The Heterogeneous Fleet Vehicle Routing Problem can be formulated as an integer linear program (ILP) or a mixed-integer linear program (MILP). The problem is difficult to solve since it has multiple constraints, including client demand, time windows, and truck capacity.

The objective is to reduce the overall cost of providing clients with goods or services while guaranteeing that each customer is attended to within a certain amount of time and that the vehicle’s capacity is not exceeded. Because of its combinatorial nature and the sheer volume of potential answers, the problem is complex and difficult to solve. 

However, several algorithms have been introduced to solve the HFVRP, that includes exact algorithms, heuristic algorithms, and metaheuristic algorithms. 

  • Exact algorithms explore the entire solution space to find the best answers. Even though they ensure optimality, they are computationally expensive and only useful for small instances. Examples of exact algorithms include branch and bound algorithms or dynamic programming.
  • Heuristic algorithms produce suboptimal solutions but are faster than exact algorithms. They sacrifice optimality for speed and efficiency. For example, Clarke and Wright’s saving algorithm or the sweep algorithm.
  • Metaheuristic algorithms utilize the search strategies of exact and heuristic methods to offer a good solution in a fair amount of time. Genetic algorithms or simulated annealing are examples of metaheuristic algorithms.

Now that we have learned about various algorithms to solve the above problem, let us now check some examples related to heterogeneous vehicle routing problems.

HFVRP Examples

Let us have a look at some real-life scenarios for the Heterogeneous Fleet Vehicle Routing Problem:

  • A courier service company might need to deliver packages to clients in various locations throughout the city using a fleet of vehicles with various sizes and price ranges. 
  • Utilizing a fleet of garbage trucks with varying costs and capacities, a waste collection company needs to collect garbage from residential areas and transport it to a landfill.
  • A school bus firm is required to carry children to various schools utilizing a fleet of buses that range in size and price.
  • A medical supply company must use a fleet of vehicles with varying sizes and prices to deliver medical equipment to hospitals and clinics spread out over the region.
  • A grocery delivery service must use a fleet of delivery trucks with different vehicle capacities and prices to deliver groceries to consumers in various parts of the city.

The aforementioned examples show the broad applicability of HFVRP and underscore the need for efficient and effective solutions to improve fleet routing and enhance the delivery of products and services.


The Heterogeneous Fleet Vehicle Routing Problem is an optimization problem that entails choosing the optimum routes for vehicles to go between a number of geographically distant locations and providing consumers with goods or services. The development of efficient algorithms and optimization techniques for the HFVRP is still an active area of research.

HFVRP is used by a variety of businesses, including courier and waste collection services, and effective solutions to this issue can lower costs, enhance customer satisfaction, and have a smaller negative environmental impact. Future developments in this field could result in more effective and sustainable logistics operations.

Author Bio
Rakesh Patel
Rakesh Patel

Rakesh Patel, author of two defining books on reverse geotagging, is a trusted authority in routing and logistics. His innovative solutions at Upper Route Planner have simplified logistics for businesses across the board. A thought leader in the field, Rakesh's insights are shaping the future of modern-day logistics, making him your go-to expert for all things route optimization. Read more.